Techniques for Empirical Mode Decomposition (EMD)-Based Noise Estimation

ABSTRACT

An Empirical Mode Decomposition (EMD)-based noise estimation process is disclosed herein that allows for blind estimations of noise power for a given signal under test. The EMD-based noise estimation process is non-parametric and adaptive to a signal, which allows the EMD-based noise estimation process to operate without necessarily having a priori knowledge about the received signal. Existing approaches to spectrum sensing such as Energy Detector (ED) and Maximum Eigenvalue Detector (MED), for example, may be modified to utilize a EMD-based noise estimation process consistent with the present disclosure to shift the same from semi-blind category to fully-blind category.

CROSS REFERENCE TO RELATED APPLICATION

The present application claims the benefit of the filing date of U.S.Provisional Application Ser. No. 62/396,290, filed Sep. 19, 2016, theentire teachings of which are hereby incorporated herein by reference.

TECHNICAL FIELD

The present disclosure relates to communication of information, and moreparticularly, to a system and method using empirical mode decompositionfor noise estimation.

BACKGROUND

Noise estimation plays a significant role in signal processing. Forinstance, RADAR and other signal detection systems utilize noiseestimation to filter or otherwise condition signals during detectionprocesses.

Other systems such as Cognitive Radio (CR) systems also utilize noiseestimation when, for instance, determining bandwidth availability. Thereis a great demand for bandwidth in wireless communications due to thedramatic shift in data usage from voice only to multimedia applications.Cognitive Radio (CR) systems were proposed as a solution to satisfy thatdemand by making the under-utilized spectrum available. Spectrum sensingis a key part CR systems, and allows secondary users (SUs) to detectspectrum owned by a licensed or primary user (PU). Different spectrumsensing methods operate at different levels of “blindness.” withblindness generally referring to the ability of a given spectrum sensorto effectively function without a priori knowledge of the PU channelstatistics, such as noise. Spectrum sensing systems must adapt to usedifferent spectrum and bandwidths based on a primary user's channelusage. Noise estimation plays a role in enhancing the performance ofnoise-dependent spectrum sensing techniques. In practice, the knowledgeof noise variance is not available and hence noise variations of thewireless channel and the thermal noise in the receiver might degrade thedetector efficacy.

The technique used for sensing the occupied and available spectrum in acognitive radio system is an important aspect of the system. Severalspectrum sensing techniques are known, each of which has advantages anddisadvantages. These techniques range from low to high computationcomplexity and have various levels of performance in determining thepresence of signals in noise.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference should be made to the following detailed description whichshould be read in conjunction with the following figures, wherein likenumerals represent like parts:

FIG. 1 is a block diagram of one exemplary embodiment of a systemconsistent with the present disclosure.

FIG. 2A is a block diagram of one exemplary embodiment of a receivingterminal consistent with the present disclosure.

FIG. 2B is a block diagram of another exemplary embodiment of areceiving terminal consistent with the present disclosure.

FIG. 3 is a block diagram of one exemplary embodiment of an EMD-basednoise estimator consistent with the present disclosure.

FIG. 4 diagrammatically illustrates operation of an EMD processconsistent with the present disclosure.

FIG. 5 includes plots of normalized frequency response of IMF₁ fordifferent values of N consistent with the present disclosure.

FIG. 6 includes plots to compare an EMD-based noise estimation processconsistent with the present disclosure with a best-fit linear regressionmodel.

FIG. 7 is a flowchart illustrating operation of one example of anEMD-based noise estimation process consistent with the presentdisclosure.

FIG. 8 is a flowchart illustrating operation of one example of anEMD-based energy detector process consistent with the presentdisclosure.

FIG. 9 includes plots showing an EMD-based noise estimation processconsistent with the present disclosure relative to a Gaussian noise-onlysignal at various SNR values.

FIG. 10 is a table showing the percentage error for an EMD-based noiseestimation process consistent with the present disclosure relative tovarious other transform-based noise estimation methods.

FIG. 11 includes plots showing performance of an energy detector (ED)modified with an EMD-based noise estimation process consistent with thepresent disclosure relative to other methods with known or true noise.

FIG. 12 includes plots showing performance of an ED modified withEMD-based noise estimation process consistent with the presentdisclosure, at an SNR of −10 dB, relative to other transform-based noiseestimation methods.

FIG. 13 includes plots showing performance of a Maximum-MinimumEigenvalue energy detector (MED) modified with EMD-based noiseestimation process consistent with the present disclosure, at an SNR of−14 dB, relative to other noise estimation methods.

FIG. 14 includes plots that show detection probability of an ED modifiedwith EMD-based noise estimation process consistent with the presentdisclosure relative to other ED methods using the DVB-T model parameterswith P_(fa)=0.01.

DETAILED DESCRIPTION

Spectrum occupancy analysis generally includes utilizing ameasured/known noise power to derive a detection threshold, andultimately determining occupancy for a channel/bandwidth under testbased on the detection threshold. Numerous semi-blind noise-estimationmethods have been proposed such as, for example, forward consecutivemean excision (FCME) and forward cell averaging (CA), which are used toestimate the level of the noise for a certain false alarm rate. Otherapproaches include using eigenvalue groups of a sample covariance matrixwhich are then split using minimum descriptive length (MDL). In theseapproaches, a goodness of lit for probability distribution function(PDF) of the noise eigenvalues is used to estimate the noise power.Still other approaches utilize Wavelet, which use Wavelet de-noising toestimate the noise power by subtracting the de-noised version from thereceived noisy signal. Each of the aforementioned methods haveparticular usage scenarios that enable relatively good performance whensignal characteristics are at least partially known, e.g., noise power.However, each is limited by noise variance, spectral efficiency, falsealarm rate, sampling rate, and adaptivity.

Thus, in accordance with an embodiment of the present disclosure, anEmpirical Mode Decomposition (EMD)-based noise estimation process isdisclosed herein that allows for blind estimations of noise power for agiven signal under test. The EMD-based noise estimation process isnon-parametric and adaptive to a signal, which allows the EMD-basednoise estimation process to operate without necessarily having a prioriknowledge about the received signal. Existing approaches to spectrumsensing such as Energy Detector (ED) and Maximum Eigenvalue Detector(MED), for example, may be modified to utilize a EMD-based noiseestimation process consistent with the present disclosure to shift thesame from semi-blind category to fully-blind category.

While aspects and embodiments specifically reference spectrum sensing incognitive radio (CR) systems, this disclosure is not limited in thisregard. For instance, the techniques disclosed herein may be implementedwithin any system that seeks to quantify noise power for a given signal.Thus, EMD-based noise estimation consistent with the present disclosuremay be applicable to wide-range of systems/devices such as, for example,RADAR systems, signal detectors, coherent detectors (e.g., ED, MED), orany system that may utilize knowledge of noise variance fordetection/operational purposes.

Turning to the Figures, FIG. 1 is a simplified block diagram of oneexample embodiment of a communication system 1 consistent with thepresent disclosure. The system 1 has been depicted as ahighly-simplified point-to-point system for ease of explanation. Thesystem 1 includes transmitting terminal 2 and a receiving terminal 6 fortransmitting and receiving signals over a communication path 10. Thecommunication path 10 may include any medium for carrying signals fromthe transmitting terminal 2 to the receiving terminal 6. For example,the communication path 10 may include one or more electrical cables,optical cables and/or the path may be a wireless path. If the path 10 isa wireless path, the transmitting terminal 2 and the receiving terminal6 may include associated antennas (not shown) for transmitting andreceiving wireless signals. Although the system is shown ascommunicating signals from the transmitting terminal 2 to the receivingterminal 6, the transmitting terminal 2 and receiving terminal 6 mayboth be configured as transceivers to allow bi-directional communicationtherebetween.

In general, the receiving terminal 6 may include an EMD-based noiseestimator for determining the noise power of a received signal. Thereceiving terminal 6 may further include an energy detector (ordetector) for detecting occupied and/or available spectral portions of abandwidth of interest. One example energy detector suitable for use inthe receiving terminal 6 is an EMD-based energy detector disclosed anddiscussed in greater detail in the U.S. application Ser. No. 14/789,398('398 application) entitled “Empirical Mode Decomposition for SpectrumSensing in Communication Systems”, which is incorporated by referenceherein in its entirety.

As used herein, the term “available” when used to describe spectrum orbandwidth shall refer to spectral portions of the bandwidth of interestthat are not carrying information signals, and the term “occupied” whenused to describe spectrum or bandwidth shall refer to spectral portionsof the bandwidth of interest that are carrying information signals.

When the system 1 is configured as a cognitive radio system, it may beconfigured for close range or long range wireless communication betweenthe transmitting terminal and the receiving terminal 2, 6 respectively.The term, “close range communication” is used herein to refer to systemsand methods for wirelessly sending/receiving data signals betweendevices that are relatively close to one another. Close rangecommunication includes, for example, communication between devices usinga BLUETOOTH™ network, a personal area network (PAN), near fieldcommunication, ZigBee networks, an Wireless Display connections,millimeter wave communication, ultra high frequency (UHF) communication,combinations thereof, and the like. Close range communication maytherefore be understood as enabling direct communication betweendevices, without the need for intervening hardware/systems such asrouters, cell towers, internet service providers, and the like.

In contrast, the term “long range communication” is used herein to referto systems and methods for wirelessly sending/receiving data signalsbetween devices that are a significant distance away from one another.Long range communication includes, for example, communication betweendevices using Wi-Fi, a wide area network (WAN) (including but notlimited to a cell phone network), the Internet, a global positioningsystem (GPS), a whitespace network such as an IEEE 802.22 WRAN,combinations thereof and the like. Long range communication maytherefore be understood as enabling communication between devicesthrough the use of intervening hardware/systems such as routers, celltowers, whitespace towers, internet service providers, combinationsthereof, and the like.

FIGS. 2A and 2B are block diagrams of example embodiments 6 a, 6 b,respectively, of a receiving terminal 6 (FIG. 1) consistent with thepresent disclosure. The block diagrams in FIGS. 2A and 2B are shown inhighly simplified form for ease of explanation. A receiving terminalconsistent with the present disclosure may include known configurationsof other components, e.g. a power supply, data modulation components,transmission components, etc., configured for receiving data signals ofa particular type depending on the application.

The embodiment 6 a illustrated in FIG. 2A includes an EMD-based noiseestimator 21, a detector 22, and a transmitter 24, such as a cognitiveradio system. In general, the EMD-based noise estimator 21 receives aninput signal 28 from the transmission path 10 (FIG. 1), and uses anEMD-based noise estimation process to provide a noise power output 25 tothe detector 22, which may be implemented as an EMD-based energydetector as discussed in the '398 application. The noise power output 25may be used to derive a detection threshold, which then may be utilizedto determine the occupancy status of a target channel(s). For instance,relative power that does not exceed the threshold indicates that thechannel is available. Therefore, the detector 22 may then receive theinput signal 28 from the transmission path (10), and use the noise poweroutput 25 from the EMD-based noise estimator 21 to provide a spectrumavailability output 26 for the input signal 28 to the transmitter 24.The spectrum availability output 26 indicates which portions of abandwidth of interest are available for use (i.e. are whitespaces) bythe transmitter 24 for communicating information signals.

The transmitter 24 uses the spectrum availability output 26 to identifyavailable spectrum and may transmit signals on the available spectrum.In an embodiment wherein the transmitter 24 is a cognitive radio system,for example, the transmitter 24 may be configured to receive input datafrom a data source (not shown) and transmit a signal or signals onavailable spectrum in response to the spectrum availability output fromthe detector 22. The transmitter 24 may be configured for transmitting asignal on available spectrum in response to the spectrum availabilityoutput of the detector 22. The transmitter 24 is shown in a highlysimplified form and may include a known RF circuit, power supply,antenna, and so on for transmitting an output signal.

The embodiment 6 b illustrated in FIG. 2B includes an EMD-based noiseestimator 21 consistent with the present disclosure coupled to adetection system 23 by way of detector 22. As described in connectionwith FIG. 2A, the EMD-based noise estimator 21 receives an input signal28 from the transmission path 110 (FIG. 1), and uses an EMD-based noiseestimation process to provide a noise power output 25 to the detector22. In turn, the detector 22 receives the input signal 28 from thetransmission path 110 (FIG. 1), and uses an energy detection process,e.g., an EMD-based energy detection process or other suitable approach,in combination with the noise power output 25 to provide a spectrumavailability output 26. The detection system 23 uses the spectrumavailability output 26 to determine portions of a bandwidth of interestthat are inappropriately carrying information signals.

For example, the detection system 23 may be configured to use thespectrum availability output 26 to identify the available spectrum inthe bandwidth of interest. The detection system 23 may then compare theavailable spectrum to an expected available spectrum to determine theextent to which the available spectrum in the bandwidth of interestdiffers from the expected available spectrum. Differences between theavailable spectrum and the expected available spectrum may indicate thatportions of the available spectrum are carrying information signals whenthey should not be carrying information signals, e.g. there isunauthorized use of frequencies or wavelengths within the bandwidth ofinterest. The detection system 23 may provide an alarm output toindicate intentional or unintentional unauthorized use of the availablespectrum.

The EMD-based noise estimator 21 and detector 22 may be provided in avariety of configurations. One example embodiment 30 of an EMD-basednoise estimator and EMD-based energy detector consistent with thepresent disclosure is illustrated in FIG. 3. The embodiment 30 includesa receiver circuit 32, a band-pass filter 34, an analog-to-digital (A/D)converter 36, an energy detector circuit 38, and an EMD-based noiseestimator circuit 39.

The receiver circuit 32 may be a known circuit configured for receivingan input signal from the communication path 110. e.g. directly from thepath or from an antenna if the signal is a wireless signal, andproviding an analog output signal representative of the received inputsignal. The analog output of the receiver circuit 32 is coupled to theband-pass filter 34. The band-pass filter 34 may take a known fixed ortunable configuration for receiving the analog output of the receiver 32and passing only portion of the bandwidth of the analog output. i.e. abandwidth of interest, to the A/D converter 36. For example, in thecontext of a cognitive radio system using an IEEE 802.22 WRAN, theband-pass filter 34 may be configured to pass only a portion of theanalog signal within the dedicated TV band specified by IEEE 802.22. TheA/D converter 36 may be configured to oversample (e.g. 10 times thehighest frequency) the output band-pass filter 34 to provide a digitaloutput representative of the output of the band-pass filter 34. Avariety of A/D converter configurations useful as the A/D converter 36are well known.

The digital output of the A/D converter 36 is coupled as an input signalto the EMD-based noise estimator circuit 39. The EMD-based noiseestimator circuit 39 receives the digital output of the A/D convener 36and provides a noise power output which indicates the noise power forthe input signal. The EMD-based noise estimator 39 implements anEMD-based noise estimation process consistent with the presentdisclosure to provide the noise power output for the bandwidth ofinterest. For example, the EMD-based noise estimator 39 may be acontroller implemented as a field programmable gate array (FPGA) and/orusing digital signal processing (DSP). As is known, DSP involvesprocessing of signals using one or more application specific integratedcircuits (ASICS) and/or special purpose processors configured forperforming specific instruction sequences, e.g. directly and/or underthe control of software instructions.

Likewise, the digital output of the A/D converter 36 may also be coupledas an input signal to the detector circuit 38. The output, e.g., noisepower output, of the EMD-based noise estimator circuit 39 may also becoupled as an input signal to the detector circuit 38. The detectorcircuit 38 may comprise, for example, an EMD-based energy detectorcircuit, although other types of detector circuits are within the scopeof this disclosure. For instance, the detector circuit 38 may comprise aRADAR circuit, a signal detector circuit, or any other type of detectorcircuit that operates at least in part on noise estimation for areceived signal.

The detector circuit 38 thus receives the digital output of the A/Dconverter 36 and the noise power output and provides a spectrumavailability output based on the same which indicates the availablespectrum in the bandwidth of interest. The detector circuit 38 may alsobe a controller, as discussed above with regard to the EMD-based noiseestimator 39.

In general, the EMD-based noise estimation circuit 39 provides noisepower output by using an EMD process, as discussed in greater detailbelow. Likewise, the detector circuit 38 may provide the spectrumavailability output by using EMD to determine frequency-domain intrinsicmode functions (IMFs).

In any event, the noise power may be derived from the signal itself,using the nature of IMFs. Likewise, the occupied spectrum may bedifferentiated from available spectrum, which is occupied only by noise,using the nature of IMFs. The IMFs may be de-noised, and a data-drivendetection threshold is calculated using the IMFs. Detection of theavailable spectrum is performed using the data-driven detectionthreshold.

EMD is a known non-linear decomposition process utilized to analyze andrepresent non-stationary real world signals. In general, EMD decomposesa time series signal into the IMFs, e.g., IMF₁ to IMF_(X), which aresimple harmonic functions collected through an iterative process. Theiterative procedure (known as sifting) eliminates most of the signalanomalies and makes the signal wave profile more symmetric. This enablesfurther processing to decompose the bandwidth of interest. The frequencycontent embedded in the processed IMFs reflects the physical meaning ofthe underlying frequencies.

In an EMD process, the IMFs of the input signal may be decomposed asIMF₁, IMF₂ and IMF₃, and so on. Relative power exceeding a noisethreshold (or detection threshold) in any channel of an IMF indicatesthat the channel is occupied. The noise threshold may be derived fromthe noise power output of the EMD-based noise estimator circuit 39.Thus, relative power that does not exceed the noise threshold in anychannel of an IMF indicates that the channel is available.

An EMD process may be implemented in a variety of ways. FIG. 4 is a flowchart illustrating one exemplary EMD process 400 useful in connectionwith a system and method consistent with the present disclosure. Whileflowcharts presented herein illustrate various operations according toexample embodiments, it is to be understood that not all of the depictedoperations are necessary for other embodiments. Indeed, it is fullycontemplated herein that in other embodiments of the present disclosure,the depicted operations, and/or other operations described herein, maybe combined in a manner not specifically shown in any of the drawings,but still fully consistent with the present disclosure. Thus, claimsdirected to features and/or operations that are not exactly shown in onedrawing are deemed within the scope and content of the presentdisclosure.

In the illustrated embodiment, the EMD process may begin by identifying402 the extrema of an input signal x(t). i.e. x_(max)(t) and x_(min)(t).An interpolation 404 between the minima points may be performed 404 todefine a lower envelope or e_(min)(t)), and an interpolation between themaxima points may be performed to define an upper envelope e_(max)(t).The averages of the upper and lower envelopes may then be calculated 406as:

m(t)=(e _(max)(t)+e _(min)(t))/2  (Equation 1)

The detailed signal may then be defined as 408 as: d(t)=x(t)−m(t). If astoppage criteria is not met 410, then the process may return to step402 to iterate using a new input signal. If the stoppage criteria 410has been satisfied, the detailed signal is assigned 412 as an IMF. Ifthe number of zero crossings is less than a selected value 414, e.g. 2,then the EMD process may end, otherwise additional IMFs may becalculated, e.g. by subtracting d(t) from the input signal to define aresidue and assigning the residue as a new input signal and iteratingthe process.

The stoppage criteria may be selected and/or applied in a number of waysto set the number of iterations in the EMD process. In one embodiment,the stoppage criteria may be selected to ensure that the differencebetween successive residue calculations is small. For example, a Cauchyconvergence test may be used to determine whether the normalized squareddifference between two successive residue calculations is less than aselected value, e.g. (0.2 or 0.3). If a given an input signal x(t) inany iteration satisfies the stoppage criteria and the number of extremaand zero crossings differ by one, then the input signal may be assignedas an IMF and the EMD process may end.

From frequency-domain perspective, EMD acts like a dyadic filter bank,where the subsequent IMFs (except for the first IMF) behave similar tooverlapping bandpass filters. The core part of the sifting processrelies on interpolating the extrema (maxima/minima) points, as discussedabove. Therefore, oversampling allows for extracting each of the localoscillations through the sifting procedure.

This disclosure has identified that the first IMF, i.e., IMF₁, may beused for noise estimation. The EMD sifting process captures the highestfrequencies in IMF₁. However, for noisy signals, IMF₁ may includelow-band frequencies (e.g, possibly PU/SU signals) when the samplingrate is not sufficient and/or the noise power is too low.

The probability distribution function (PDF) of IMF₁ for an inputGaussian processes is a mix of two normal distributions represented bythe Gaussian mixture (bimodal) distribution. The justification of thebi-modality in such a distribution lies in the large discrepancy ofvalues (in case of noisy or noise only signals) yielded by the maximaand minima envelops. The first IMF, denoted by c₁(n), follows the PDF:

$\begin{matrix}{{f\left( {c_{1}(n)} \right)} = {{\frac{ɛ}{\sqrt{2{\pi\sigma}_{u}^{2}}}e^{- \frac{{({{c_{1}{(n)}} - \mu_{u}})}^{2}}{2\sigma_{u}^{2}}}} + {\frac{1 - ɛ}{\sqrt{2{\pi\sigma}_{l}^{2}}}e^{- \frac{{({{c_{1}{(n)}} - \mu_{l}})}^{2}}{2\sigma_{l}^{2}}}}}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

where μ_(u), σ_(u), μ_(l), σ_(l) are the mean and the standard deviationfor upper and lower mode distributions respectively, and ε∈[0,1]represents the mode distribution weight.

As discussed above, IMFs can be interpreted as a dyadic filter bank thatresembles the behavior of wavelets. However, unlike the filteringproperties of wavelets, the EMD non-linear decomposition processintroduces different cutoff frequencies.

FIG. 5 illustrates the normalized frequency response for the powerspectral density (PSD) of c₁(n) of a noise only input signal w(n) for5000 averaged trials. This figure shows the adaptive high-pass filteringcharacteristic of IMF₁ and how the sampling rate impacts the cutofffrequency. The first IMF, under sufficient sampling rates, is dominatedby noise and thus can be exploited to estimate the noise power of areceived signal.

An empirical ratio of the first LMF power to the total noise power ofthe received signal denoted by β is:

$\begin{matrix}{\beta = \frac{{\hat{\sigma}}_{c_{1}}^{2}}{\sigma_{w}^{2}}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

where {circumflex over (σ)}_(c) ₁ ² is the estimated variance of c₁(n)and σ_(w) ² is the total noise power of the received signal.

The first IMF, c₁(n), may be modeled as a bimodal zero-mean normalprocess with a variance of σ_(c) ₁ ² i.e. c₁(n)˜

(0, c_(c) ₁ ²). The variance of each mode distribution in Equation (2)is estimated using maximum-likelihood parameter estimation viaExpectation Maximization (EM) algorithm. The estimated overall varianceof IMF₁, denoted by {circumflex over (σ)}_(c) ₁ ², may be given as:

{circumflex over (σ)}_(c) ₁ ²=ε{circumflex over (σ)}_(u)²+(1−ε){circumflex over (σ)}_(l) ²+ε(1−ε)({circumflex over(μ)}_(u)−{circumflex over (μ)}_(l))²  (Equation 4)

where {circumflex over (σ)}_(u) ², {circumflex over (σ)}_(l) ²,{circumflex over (μ)}_(u) and {circumflex over (μ)}_(l) are theestimated variances and means of the upper and lower mode distributions.

The bi-modality of c₁(n) can be attributed to the inherent switchingbetween two mutually exclusive Gaussian processes of different means.For simplification, the mode distribution weight ε is assumed to be 0.5and that assumption is rationalized by the fact that maxima and minimaof the upper and lower envelopes are almost equally likely andsymmetrically distributed around the zero overall mean of the signal.

Analytically, the scaling factor β can be expressed as the ratio ofintegrating the PSD of IMF₁ and the received signal, r(n)=w(n), in termsof extrema (maxima/minima) distribution. The extrema are equally spacedwith the maxima being located at integer time instants and the minima athalf the distance between a pair of consecutive maxima. For the case ofcubic spline interpolation, the frequency response of the unit spacedknots l(v) may be given as:

$\begin{matrix}{{I(v)} = {\left( \frac{\sin\;\pi\; v}{\pi\; v} \right)^{4}\frac{3}{2 + {\cos\; 2\pi\; v}}}} & \left( {{Equation}\mspace{14mu} 5} \right)\end{matrix}$

The PSD of the first IMF, S_(c) ₁ (v), may be given by:

S _(c) ₁ (v)=|(1−I(3v))|² S _(w)(v)(0≤v<½)  (Equation 6)

where S_(w)(v) is the PSD of the received signal w(n). Thus, thecorresponding ratio {circumflex over (β)} may be given by:

$\begin{matrix}{\hat{\beta} = \frac{\int_{0}^{1/2}{{S_{c_{1}}(v)}{dv}}}{\int_{0}^{1/2}{{S_{w}(v)}{dv}}}} & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$

The scaling factor, {circumflex over (β)}, as given in Equation (7) isthe result of the first iteration (through the sifting process) toobtain IMF₁. The {circumflex over (β)} in Equation (7) is not as genericas the one given in Equation (8) however, it is presented here toprovide further validating evidence for the EMD-based noise estimatorapproach disclosed herein.

The ratio, β, plays the role of a scaling factor that can be used toestimate σ_(w) ². FIG. 6 shows a comparison of β, dashed line, to thebest fit linear regression model, solid line, when r(n)=w(n). Thisdisclosure has identified that β can be approximated by a simplefunction of the sample size, N, of the received signal:

β(N)=S log₂(N)+β(1)  (Equation 8)

where β(1) is the y-intercept of the best fit linear model usingpolynomial least-squares and S is the linear fit slope. From FIG. 6, thesample size, N, is represented logarithmically in order to linearize thetrend of β.

These β values maintain a linear trend over different sample size valuesand validate the model in Equation (8). According to Equation (8), andfor a sample size N, the estimated noise power, {circumflex over(σ)}_(w) ², of the received signal r(n) can be given as:

$\begin{matrix}{{\hat{\sigma}}_{w}^{2} = \frac{{\hat{\sigma}}_{c_{1}}^{2}}{\beta(N)}} & \left( {{Equation}\mspace{14mu} 9} \right)\end{matrix}$

In summary, therefore, the EMD-based noise estimation circuit 39consistent with the present disclosure may use an EMD process todetermine the total noise power of a received signal. FIG. 7 is a flowchart illustrating one exemplary embodiment 70 of an EMD-based noiseestimation method that may be performed by an EMD-based noise estimatorcircuit consistent with the present disclosure. Exemplary details of theoperations shown in FIG. 7 are discussed above. As shown, the method 70includes determining 71 an empirical ratio of the first IMF power to thetotal noise of the received signal using, for example, Equation (3),estimating 72 power of the received signal based on the determinedempirical ratio, and providing the estimated noise power (which may alsobe referred to as a noise power estimate, noise power output, or simplynoise power).

Continuing on, and from the context of the detector circuit 38 (FIG. 3)being an EMD-based energy detector, once the IMFs are calculated and thebandwidth of interest is confirmed to be either entirely vacant, i.e.the entire bandwidth may be considered available spectrum, or to includeat least one occupied channel, the IMFs may be de-noised by filtering orsmoothing. De-noising may be advantageous in an embodiment of a systemand method consistent with the present disclosure when there is a largevariation of the magnitudes of different IMFs associated with a signal.Large variations in IMF magnitudes may affect the derivation of thethreshold used for detection.

To de-noise the IMFs, a filter, such as a known Savitzky-Golay (S-G)filter, or polynomial smoothing may be applied to the IMFs. An S-Gfilter, for example, is a generalization of a finite-impulse-response(FIR)-averaged filter with non-linear characteristics. An S-G filter maybe used to reduce noise while maintaining the shape and height of theIMF waveforms. Spectral peaks in the IMFs due to the noise power mayhave a negative influence on the setting of the threshold. Accordingly,the frame size and the polynomial order of the S-G filter may beselected to provide smoothing of the peaks while retaining the spectralheight of the IMFs. Selecting a low or high order filter with a smallframe size may yield poor smoothing. However, increasing the filterorder with relatively large frame size has been found to produce bettersmoothing and retain the spectrum height. In one embodiment, forexample, it has been found that an S-G filter with a polynomial of thirdorder and a frame size of 41 achieved a tradeoff between the IMF heightsand the smoothing of the IMFs in their frequency-domain representation.The filtered IMFs can be represented as:

$\begin{matrix}{{{\overset{\_}{C}}_{i}(f)} = {{j!}{\sum\limits_{m = {- K}}^{K}{{g_{j}\left( {- m} \right)}{{\hat{C}}_{i}^{(j)}\left( {f - m} \right)}}}}} & \left( {{Equation}\mspace{14mu} 10} \right)\end{matrix}$

where C _(i) is the filtered signal of i^(th) IMF, K is the frame size,g_(j) is the polynomial coefficient, and j is the polynomial order.

Therefore, in a system and method consistent with the present disclosurethe filtered IMFs may be reconstructed and compared against adata-driven threshold (or detection threshold) derived from the noisepower output received from an EMD-based noise estimator, e.g., theEMD-based noise estimator circuit 39 (FIG. 3). The data-driven thresholdmay be determined adaptively using the process 70 of FIG. 7, forexample.

Once the data-driven threshold is determined the filtered IMFs may bereconstructed according to:

$\begin{matrix}{{C_{r}(f)} = {\sum\limits_{i = 1}^{M}{C_{i}(f)}}} & \left( {{Equation}\mspace{14mu} 11} \right)\end{matrix}$

The reconstruction of the IMs, C_(r)(f), is compared to the calculatedthreshold λ_(d) to determine whether portions of the bandwidth ofinterest occupied or available.

In summary, therefore, the detector circuit 38 consistent with thepresent disclosure may use an EMD process and the data-driven threshold.e.g., estimated noise power from the EMD-based noise estimation circuit39, to determine whether portions of a bandwidth of interest compriseavailable spectrum or occupied spectrum. Note, the detector circuit 38may also implement other known spectrum analysis circuits and thisdisclosure should not be construed as limiting in this regard.

FIG. 8 is a flow chart illustrating one exemplary embodiment 80 of anEMD-based energy detection method that may be performed by an EMD-basedenergy detector circuit consistent with the present disclosure.Exemplary details of the operations shown in FIG. 8 are discussed above.As shown, the method includes filtering 81 a bandwidth of interest usinga band pass filter (e.g. filter 34 in FIG. 3), and then decomposing 82 adigital time domain version of the filtered output using an EMD process.The IMFs obtained using the EMD process may then be represented 83 inthe frequency domain, e.g. according to:

$\begin{matrix}{{{\hat{C}}_{i}(f)} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{{{C_{i}(n)}e^{\frac{{- 2}\pi\;{ifn}}{N}}}}^{2}}}} & \left( {{Equation}\mspace{14mu} 12} \right)\end{matrix}$

where N is number of samples of the digital time domain signal x(n), fis a number of frequency bins, and Ĉ_(i) is the i^(th) frequency-domainIMF. Each IMF may then be filtered 84 to remove noise. e.g. using a S-Gfilter of the third order, and the data-driven threshold λ_(d) may bedetermined 85 based on the estimated noise power. e.g. using theEMD-based noise estimator circuit 39. The filtered IMFs may then bereconstructed 86, e.g. according to equation (11), and the reconstructedIMFs may be compared 87 to the threshold. If any selected channel orother portion of the bandwidth of an IMF exceeds the threshold, thechannel is deemed to be occupied. Otherwise, the channel or bandwidth isavailable spectrum that is available for use. A spectrum availabilityoutput may then be provided 88.

Experimental Methodologies and Results

Consistent with aspects of the present disclosure a signal-driven (ordata-driven) noise power estimation method/process is variouslydisclosed herein. The following experimental results were based ontransitioning two known detector implementations, namely forwardconsecutive mean excision (FCME) and Wavelet, from semi-blind tofully-blind, which is to say from approaches that require some amount ofa priori knowledge about a target signal to approaches that leverage theEMD-based noise estimation techniques disclosed herein to operatefully-blind.

The EMD-based noise estimation techniques disclosed herein takeadvantage of an observed unique ratio, β, between the IMF₁ power and thetotal noise power in the received signal. The performance of theproposed EMD-based noise estimation process was further tested throughupgraded/modified detectors and the results are compared to otherestimation schemes, as discussed further below. The proposed noiseestimation method disclosed herein outperforms other schemes at low SNRacross a range of signal types.

The following assumes a configuration of one primary user (PU) and onesecondary user (SU) node with an additive white Gaussian noise (AWGN)channel and a single channel spectrum scanner with a band pass filter(BPF). An OFDM-modulated communication signal is synthesized with aknown noise power. The results are carried out through a Monte-Carlosimulation by averaging 2000 runs.

First, we show the boundaries of the EMD-based noise estimation process(β) variously disclosed herein under different values of Signal-to-NoiseRatio (SNR) and sampling rates, Nyquist rate, (N_q=2f_max). In FIG. 9, areceived Gaussian noise-only signal 90 (dotted gray line) is used as areference to compare the same with the scenario of a noisy signal.

From FIG. 9 the results demonstrate that for low sampling rates β fromEquation (8) will perform relatively well only at low SNR values, e.g.,at about <−8 dB, as the noise will dominate the signal and closelyresemble a noise-only signal scenario. However, for higher samplingrates, e.g., ≥ to about 8N_q, β will perform in a very similar way tothe noise-only case. The deviation of β at low sampling rate and highSNR values occurs because IMF₁ sifts part of the signal in addition tothe noise and increases the corresponding variance. Therefore, to ensurethe proper functionality of the proposed β model at wide range of SNRvalues, oversampling was considered a requirement for the test signalsutilized herein.

The EMD-based noise estimation model of equation (8) was furtherevaluated using a percentage error metric in which the true noise,σ_w{circumflex over ( )}2 of the received signal was used as areference. FIG. 10 includes a table 10 that shows a comparison betweenthe proposed β model and two other transform-based estimationtechniques: Forward consecutive mean excision (FCME) and Wavelet noiseestimation methods. Table 10 shows that at low SNR values (<−10 dB) boththe FCME and wavelet methods performed slightly better than the proposedmethod. However, both methods exhibit a rapid degradation in the noiseestimation performance as the SNR increases (≥−10 dB) and that isexpected due to the domination of the signal features over the noise inwhich these techniques fail to differentiate the signal from the noise.In comparison, β method, i.e., the EMD-based noise estimation approachvariously disclosed herein, has steady performance over all SNR valuesexcept at SNR≥10 dB where IMF₁ starts to sift signal components inaddition to the noise. The degradation of the proposed model can bemitigated by increasing the sampling rate, which guarantees that IMF₁will be predominantly populated by noise samples only.

In FIG. 11, a graph 1100 illustrates the performance of ED modified withan EMD-based noise estimator (β) relative to a conventional FCME andWavelet approach. In FIG. 11, the probability of detection, P_(d), isused as a metric to evaluate the performance of each approach with theknown or true noise with pobability of false alarm, P_(fa) at 0.1 andSNR=−12 dB. As shown, the β approach performs substantially as well asthe truse noise particularly at a low number of samples.

The Receiver Operating Characteristic (ROC) was also used as aperformance metric for both ED and MED using different noise estimationmethods in which 2000 samples represent a sensing cycle of 625 μs at8N_q. The SNRs in FIGS. 12 and 13 were chosen to best reflect theperformance of each method in real-world circumstances.

In FIG. 12, a graph 1200 shows performance of an ED modified with anEMD-based noise estimator (β), at −10 dB, relative to differenttransform-based noise estimation methods (e.g., Wavelet, FCME andMaximum-Minimum Eigenvalue noise estimator denoted as ┌10┐) as well as amodel-based method with a smoothing factor of 50.

In FIG. 13, a graph 1300 illustrates the performance a MED techniquemodified with an EMD-based noise estimator (β) at SNR of −14 dB for thesame noise estimation methods as shown in FIG. 12. For comparison, afully-blind spectrum sensing technique, Maximum-Minimum Eigenvalue(MME), computed with 6000 samples was added to FIG. 13.

As shown in FIGS. 12 and 13, it is demonstrated that the EMD-based noiseestimation approach (β) of the present disclosure outperforms otherestimators in addition to the MME technique which requires a much highersampling rate. The β approach performs close to true noise for theassigned SNR value and number of samples. In addition, the degradationof other method's performance is due to the estimation error as SNRvalues increase. While Wavelet and FCME show slightly better noiseestimation error (see FIG. 10) compared with the β approach of thepresent disclosure, that does not mean they can be used for very low SNRdetection. The reason is that for the number of samples used during theaforementioned simulations, each detector will have an SNR wall that cannot be exceeded even if the number of samples is increased infinitely.

Finally, the performance of the proposed EMD-based noise estimationapproach of the present disclosure was compared to the noise estimationgiven using ED. FIG. 14 shows a graph 1400 that illustrates thedetection probability of the ED methods using the DVB-T model parameterswith P_fa=0.01. In addition, the noise uncertainty (1 dB) is presentedto reveal the effect of noise fluctuation on the detector performance.The ED with the true noise exhibits the best performance in contrast tothe worst performance of 1-dB noise uncertainty. The EMD-based noiseestimation approach of the present disclosure shows a slightly betterperformance compared to pilot periodicity noise estimation denoted as[27]. Unlike pilot periodicity noise estimation [27], which isspecifically designed for DVB-T signals, the proposed EMD-based noiseestimation approach can work for a wider range of modulation schemes.

One aspect of the present disclosure discloses a system, the systemcomprising an empirical mode decomposition (EMD)-based noise estimatorto decompose a received signal into a plurality of intrinsic modefunctions (IMFs) and provide a noise estimation output based on theplurality of IMFs, the noise estimation output being based at least inpart on a ratio (β) of a power of a first IMF of the plurality of IMFsto a total noise power of the received signal.

Another aspect of the present disclosure discloses a method ofestimating noise power in a signal of interest. The method comprisingreceiving, by a controller, a signal, decomposing, by the controller,the received signal into a plurality of intrinsic mode functions (IMFs)using an empirical mode decomposition (EMD) process, the plurality ofIMFs comprising IMF₁ to IMF_(X), determining, by the controller, a ratio(β) of IMF₁ power to a total noise power of the received signal, anddetermining, by the controller, a noise power output based on the ratio(β).

Another aspect of the present disclosure discloses an EMD-based methodof estimating noise power in a bandwidth of interest. The methodcomprising receiving, by a controller, a signal comprising a bandwidthof interest, decomposing, by the controller, the signal into a pluralityof intrinsic mode functions (IMFs) using an empirical mode decomposition(EMD) process, the plurality of IMFs comprising IMF₁ to IMF_(X),determining, by the controller, a ratio (β) of IMF₁ power to a totalnoise power of the received signal, determining, by the controller, anoise power output based on the ratio (β), determining, by thecontroller, a detection threshold based on the noise power output, andcomparing each IMF of the plurality of IMFs to the detection thresholdto determine which portions of the bandwidth of interest are availablespectrum.

Embodiments of the methods described herein may be implemented using aprocessor and/or other programmable device. To that end, the methodsdescribed herein may be implemented on a tangible, computer readablestorage medium having instructions stored thereon that when executed byone or more processors perform the methods. Thus, for example, thetransmitter and/or receiver may include a storage medium (not shown) tostore instructions (in, for example, firmware or software) to performthe operations described herein. The storage medium may include any typeof non-transitory tangible medium, for example, any type of diskincluding floppy disks, optical disks, compact disk read-only memories(CD-ROMs), compact disk re-writables (CD-RWs), and magneto-opticaldisks, semiconductor devices such as read-only memories (ROMs), randomaccess memories (RAMs) such as dynamic and static RAMs, erasableprogrammable read-only memories (EPROMs), electrically erasableprogrammable read-only memories (EEPROMs), flash memories, magnetic oroptical cards, or any type of media suitable for storing electronicinstructions.

It will be appreciated by those skilled in the art that any blockdiagrams herein represent conceptual views of illustrative circuitryembodying the principles of the disclosure. Similarly, it will beappreciated that any flow charts, flow diagrams, state transitiondiagrams, pseudocode, and the like represent various processes which maybe substantially represented in computer readable medium and so executedby a computer or processor, whether or not such computer or processor isexplicitly shown. Software modules, or simply modules which are impliedto be software, may be represented herein as any combination offlowchart elements or other elements indicating performance of processsteps and/or textual description. Such modules may be executed byhardware that is expressly or implicitly shown.

The functions of the various elements shown in the figures, includingany functional blocks, may be provided through the use of dedicatedhardware as well as hardware capable of executing software inassociation with appropriate software. When provided by a processor, thefunctions may be provided by a single dedicated processor, by a singleshared processor, or by a plurality of individual processors, some ofwhich may be shared. Moreover, explicit use of the term “processor” or“controller” should not be construed to refer exclusively to hardwarecapable of executing software, and may implicitly include, withoutlimitation, digital signal processor (DSP) hardware, network processor,application specific integrated circuit (ASIC), field programmable gatearray (FPGA), read-only memory (ROM) for storing software, random accessmemory (RAM), and non-volatile storage. Other hardware, conventionaland/or custom, may also be included.

As used in any embodiment herein, “circuit” or “circuitry” may comprise,for example, singly or in any combination, hardwired circuitry,programmable circuitry, state machine circuitry, and/or firmware thatstores instructions executed by programmable circuitry. In at least oneembodiment, the transmitter and receiver may comprise one or moreintegrated circuits. An “integrated circuit” may be a digital, analog ormixed-signal semiconductor device and/or microelectronic device, suchas, for example, but not limited to, a semiconductor integrated circuitchip. The term “coupled” as used herein refers to any connection,coupling, link or the like by which signals carried by one systemelement are imparted to the “coupled” element. Such “coupled” devices,or signals and devices, are not necessarily directly connected to oneanother and may be separated by intermediate components or devices thatmay manipulate or modify such signals. As used herein, use of the term“nominal” or “nominally” when referring to an amount means a designatedor theoretical amount that may vary from the actual amount.

While the principles of the disclosure have been described herein, it isto be understood by those skilled in the art that this description ismade only by way of example and not as a limitation as to the scope ofthe disclosure. Other embodiments are contemplated within the scope ofthe present disclosure in addition to the exemplary embodiments shownand described herein. Modifications and substitutions by one of ordinaryskill in the art are considered to be within the scope of the presentdisclosure.

1-16. (canceled)
 17. A system for noise estimation of a signal usingempirical mode decomposition (EMD) comprising: a controller configuredto: decompose the signal into a plurality of intrinsic mode functions(IMFs); determine a noise power of a first IMF of the plurality of IMFs;and output an estimated total noise power for the signal based at leastin part on the determined noise power of the first IMF of the pluralityof IMFs.
 18. The system of claim 17, wherein the estimated total noisepower of the signal is based at least in part on an empirical ratio βdefined as: $\beta = \frac{{\hat{\sigma}}_{c_{1}}^{2}}{\sigma_{w}^{2}}$where {circumflex over (σ)}_(c) ₁ ² is an estimated variance of c₁(n)and σ_(w) ² is a total noise power of the signal.
 19. The system ofclaim 18, wherein the EMD-based noised estimator determines a scalefactor based on the empirical ratio (β), and wherein the estimated totalnoise power is based on multiplying the noise power of the first IMF bythe scale factor.
 20. A method of estimating noise power of a signal,the method comprising: receiving, by a controller, a signal having aselected channel or bandwidth of interest; decomposing, by thecontroller, the received signal into a plurality of intrinsic modefunctions (IMFs) using an empirical mode decomposition (EMD) process,the plurality of IMFs comprising IMF₁ to IMF_(X); determining, by thecontroller, a ratio (β) of IMF₁ power to a total noise power of thereceived signal; determining, by the controller, an estimated noisepower for the signal based on the ratio (β); and outputting, by thecontroller, the estimated noise power to a detector.
 21. The method ofclaim 20, further comprising: determining, by the controller, adetection threshold based on the estimated noise power; and comparing atleast one IMF of the plurality of IMFs to the detection threshold todetermine the selected channel or bandwidth of interest is occupied. 22.The method of claim 21, further comprising reconstructing the pluralityof IMFs, and wherein comparing the at least one IMF to the detectionthreshold includes comparing each IMF of the reconstructed IMFs to thedetection threshold.
 23. The method of claim 20, wherein the ratio (β)is given by: $\beta = \frac{{\hat{\sigma}}_{c_{1}}^{2}}{\sigma_{w}^{2}}$where {circumflex over (σ)}_(c) ₁ ² is an estimated overall variance ofIMF₁ and σ_(w) ² is the total noise power of the received signal. 24.The method of claim 23, wherein outputting the estimated noise power tothe detector further comprises outputting the estimated noise power toan energy detector (ED).